In each case either prove the statement or give an example showing that it is false. (a)

Question:

In each case either prove the statement or give an example showing that it is false.
(a) If || - || = 0, then = .
(b) If |||| = ||||, then = .
(c) If = t for some scalar t, then and have the same direction.
(d) ||-5|| = -5|||| for all .
(e) ||+ || = |||| + |||| for all and .